Hi,

I have a game theory question, probably pretty simple, but it is still not clear for me.

- What is the connection between range advantage and sizing? How are these related?

- How come the equity in this picture?
- What about my range distribution?

I mean I made a lot of gto analysis and found unusual things which was hard to explain.
For example:

btn v bb overbet cbet is the maxEV on 689
(we have range disadvantage here)

Or

utg v btn overbet cbet on 444
But only 1/4 cbet on AAK
(we have range advantage on both)


So I would be really glad if somebody could explain the proper relation of these terms and the relations between them.
Maybe I start an interesting discussion with this

Definitely would like to hear some answers.
OP you said board 1 we have range disadvantage and 2-3 advantage. What were the equities and evs of the 3 situations?

I would think board 1: Equity and nut advantage roughly equal but rfi has position so will probably have like 60+ % EV
board2: eq advantage fairly big but position subtracts substantial ev
board3: eq advantage not so big and position subtracts substantial ev

As far as sizing and nut advantage

Board 1:
No nut advantage. Why overbet? Is it because our betting frequency is so low due to equity being so close? Value is urgent because we wont be able to valuebet most turns/rivers?

Board 2: We have all the super nut combos and a good chunk of semi nut combos that are still beaten by the frequent AQ AJs ATs in cold callers range we have a lot of hands that want to put money in the pot for value that are can still be beaten by ip cold caller.

Board 3: Depending on the range of the opener and caller but generally ip should be doing well in equity(condensed range that contains less air) and ev(because of position) but contains non of the nut combos that the pfr has.

The pfr has alot of air and equity advantage is probably marginal compared to AAK flop. Id think the closer eq makes oop bet less on this board than board2. In addition the amount of air pfr has in suited aces, offsuit AT+ and connectors combined with all the nut combos probably makes this a highly polarized nuts/air vs bluffcatcher spot where oop highest ev comes from maximizing number of bluffs, their fold equity and being able to bomb away with JJ+ being the immortal nuts.

These are just my ideas and would like a wise man to clarify how equity and ev, position and nut combos affect sizing. So far I think equity determines how often we bet. Nut concentration and polarity of range increases sizing, but still somewhat confused about it all

Thx

It's not just about range advantage, nut concentration, or polarity. You also have to consider villain's counter-strategy to each sizing, as the sizing will affect what hands villain can continue with.
Sometimes your range/strategy maximises EV by betting big, even if it causes villain to "overfold" (i.e. at greater than minimum-defence frequencies), and sometimes you maximise EV by getting called at a high frequency.
It's easiest to comprehend on the river, where you'll typically bet big and go polar if you're in a nuts/air vs bluffcatchers situation, but small when you have a lot of "thin value" hands, but the principle also exists to some extent on the earlier streets.
I'll write a bit more about this tomorrow, making reference to the flops you mentioned.

e.g. with the 444 flop, it might be the case that 2x pot is the max EV size, because although you can't c-bet at a high frequency for that size, villain can only continue with JJ-99, and those hands are in terrible shape against QQ+, and will be in bad shape on Ax/Kx/Qx turns, as your bluffs are with overcards. To put it another way, the last thing villain's range wants to face on a 444 flop is an overbet; so that's possibly the size you should go with.
On boards like AAK where he has some draws that can call a small bet, it's apparently better to go smaller to get value with a bigger chunk of your range. Some of villain's range can't continue even vs a small bet on the AAK flop, so you can "get away with" cheap bluffs, and you also don't get stacked when you're betting AJ/AT and run into AQ.

I'm really not sure about the 986 board. Have you got a screengrab showing that an overbet is correct? I'd like to know the range you have for the BB, and also whether he has a donking strategy. FWIW, Snowie liked a pot-sized c-bet in the 100NL sim I looked at, but I don't think the EV is massively different to picking a smaller size and using a wider betting range. That board is certainly a lot harder to "compute" than the others you mentioned, since there are so many combos (in both ranges) that connect with it in some way or other. On the 444 flop, both players have boats or air (and some quads for UTG), but UTG's boats completely destroy the BTN's.

Sorry for the delay and thank you for the answers I try to build in to my thinking.

I remembered wrong about the 3rd board.
I checked my calculations again, and for BTNvBB overbet boards was for example T84 with fd, K96 with fd, and AKx boards.

Of course the EV of the overbet was pretty close to the EV of 3/4 bet.

BB range:


I did not add donking range.
As I see so far there is no exact answer to these relations and it is more complex than I thought. But maybe we figure out something.